Impact of training on multiple-antenna communications in wireless ad hoc networks

We investigate the impact of channel estimation when employing point-to-point multiple-input single-output beamforming in stochastic ad hoc networks. We first derive a new outage probability expression with a linear minimum-mean-square-error estimator, and then characterize the feasible range of the pilot-training length and outage level pair to achieve a positive transmission capacity. Finally, for a sufficiently small outage constraint and sufficiently long frame length, we derive the optimal pilot-training length that maximizes the transmission capacity, which is shown to increase with the number of transmit antennas.